Who is this course for?
Numerical methods are a part of the problem solving skills that are expected to be mastered by most of the university graduates working in a quantitative field. The same fundamental concepts of Brownian motion, convection, diffusion, dispersion and non-linearity are used to simulate applications in telecommunication (collisions of data-packets in a network, solitons in optical fibers), economics (stock options), biology (transport in cellular tissues), engineering (heat transfer, pollution) and social sciences (behavior of people in a crowd). Quantitative answers for real applications can generally be obtained only from computations.

What are the course targets?
The goal is to cover a wide range of numerical methods with simple examples to analyze building blocs that are used in complex simulation codes. A broad knowledge is often decisive to choose the right method when developing a new code. A strong emphasis is put on the problem based learning where the participants analyze data, derive, implement, document and execute their own models in a web browser everywhere on the Internet.
The course covers finite-differences, finite-elements, Fourier and Monte-Carlo methods and Lagrangian schemes; in each case, the algorithm is illustrated with prototype problems including the Fokker-Plank (transport), Black-Scholes (stock options), Burger (shock waves), Korteweg-DeVries (solitons) and Schrödinger equations.
Students who fulfill the course requirements obtain 4 Ladok / 6 ECTS credit points in the Swedish academic system or a course certificate showing that they met all the requirements to pass the postgraduate course for an equivalent of 4 weeks full time work -- an accreditation to reward professionals even within their own company.

Prerequisites.
To benefit from most of the material, participants need to have a basic knowledge in differential calculus, complex analysis and need to have a rough idea of what is a Fourier transformation. Few of these analytical techniques will be used, since most are carried out with the computer; the underlying concepts, however, remain the same and will not be exposed. Elementary programming is sufficient to modify templates and pick-up the knowledge in LaTeX, Java and HTML used to hand-back the assignments at a distance.

Flexible self-learning environment.
Apart from a tutorial that may be organized locally at the begining of a the Netuniversity course, all the material and the human support is accessible anytime from anywhere via the Internet. Each module corresponding to a chapter in the syllabus has its own set of assignments: they are carried out when time allows and are submitted for correction to a human teacher directly from a web browser. Help is provided by teachers and other participants in the classroom forum; this is where students meet informally and create professional contacts. The problem based self-learning environment used in this course is particularly well suited for a lifelong learning students who have professional obligations and cannot attend classes on a regular basis.

Admission, tuition fee, sponsorship.
Graduate students affiliated with a public university in Europe can participate free of charge in the Netuniversity course sponsored by the Swedish government (see below). Self-learners from sister universities and developing countries (who cannot easily afford to pay the price of a book) are sponsored by Lifelong-learners: they are warmly encouraged to register free of charge. Other learners who want to study outside the Netuniversity course period have to pay a fee for their teaching support.

Distance learning schemes

Our cyber tutoring remains accessible throughout the year; continued education with human support outside the academic framework is however not formally offered nor supported by the Royal Institute of Technology. A paying service is maintained by the teachers and can be accessed from this website. To open an account and start studying, all you need is to complete the registration form with a valid e-mail address where we can send your password and maintain a regular contact with you. A variety of learning schemes are designed to provide different levels of support and depend whether you are affiliated with a university or not.

Free-learning (for universities & developing world)
Self-learners from sister universities and the developing world (who cannot easily afford to pay the fee of a book) have been sponsored by Lifelong-learners since 1999 and are warmly welcome to register free of charge; others are kindly requested to register for a paying scheme.

Open-learning (for everyone)
Distance learning services with or without support are offered throughout the year under this link. The same material is taught by the same teachers as in the university, providing additional flexibility for the enrollement, the duration of the course and the strict academic requirements.

Special courses planned during the year 2005

These courses are organized in collaboration with top level universities or companies and are limited in time.

Swedish Netuniversity (10 October - 16 December 2005, 4pts, 6ECTS)
This is the regular course taught at the Royal Institute of Technology (KTH) internally to graduate students (2D5246), externally to continued education students (2D4232) and is free of charge for graduate students who are affiliated with a public university in Sweden or abroad. Apart from an initial welcome lecture that is given at KTH in Stockholm, the course can be completed entirely at a distance within the Swedish Netuniversity context. To register, qualifying participants have both to fill-in an application form (preferably before 15 May) and to open an account anytime on the dedicated website.

Doctoral school, Ecole Polytechnique Fédérale de Lausanne (10 October - 16 December 2005, 6ECTS)
A doctoral course has been organized in 2001 and 2003 in a partnership between Laurent Villard (EPFL) and André Jaun (KTH) and will be taught again during 2005. Students contact their local respondant for an up-to-date information and complete their registration on-line without forgetting to specify their complete date of birth (dd-mm-yyyy) to allow for the transfer of academic credits.

Private companies and firms
The list can not be disclosed here; specific information will be displayed on your Intranet if a course is organized. If you would like to organize such a course, please contact André Jaun (tel: +46 70 7971879) to enquire about the possibilities.